Various types of microstructural architectures, including multi-material architectures that achieve superior thermal properties (e.g. extreme thermal expansion coefficients) from those of naturally occurring materials are known. Example types are described in, for example, (a) Lakes, R., Cellular solid structures with unbounded thermal expansion. Journal of Materials Science Letters, 1996. 15(6): p. 475-477; (b) Sigmund, O. and S. Torquato, Composites with extremal thermal expansion coefficients. Applied Physics Letters, 1996. 69: p. 3203; (c) Jefferson, G., T. A. Parthasarathy, and R. J. Kerans, Tailorable thermal expansion hybrid structures. International Journal of Solids and Structures, 2009. 46(11-12): p. 2372-2387; (d) Steeves, C. A., et al., Concepts for structurally robust materials that combine low thermal expansion with high stiffness. Journal of the Mechanics and Physics of Solids, 2007. 55(9): p. 1803-1822; (e) Cribb, J. L., Shrinkage and Thermal Expansion of a Two Phase Material. Nature, 1963. 220: p. 576-577; and (f) Lakes, R., Cellular solids with tunable positive or negative thermal expansion of unbounded magnitude. Applied Physics Letters, 2007. 90: p. 221905.
The basic topologies for many such microstructural architectures were, however, generated by way of creative thought and then their geometric parameters and material properties were later optimized using analytical expressions tailored to their specific topologies. No systematic analytical approach existed, which was capable of generating such design concepts from scratch. Designers, therefore, relied on topology optimization to numerically generate microstructural architecture concepts. Topology optimization utilizes a computer to iteratively construct a microstructural architecture that possesses properties, which most closely approach the desired target properties while satisfying specific constraint functions. The design space begins with an unorganized mixture of desired materials and a cost function is minimized until an optimal microstructural architecture is achieved, which consists of organized clumps of the materials. One of the biggest problems with topology optimization and the designs produced thereby is that designer can never be certain that the most optimal concept was identified. The cost function often bottoms out inside a local minimum instead of the global minimum, which corresponds to the truly optimal microstructural architecture. Furthermore, it is difficult to know which constraint functions to impose on the optimization, as vastly different concepts are generated depending on the constraint functions that are applied. Often, the computer generates microstructural architectures that possess impractical features, which are not possible to fabricate or implement. The reason for this deficiency is that the computer is not able to apply commonsense or creativity during the optimization process to recognize or generate functional concepts with practical features.